{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sigmoid Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "z = np.linspace(-10, 10, 1000)\n",
    "a = sigmoid(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KRUGkh+w4UMPiLQe060hSmoqCSA/RriNJByoKIj3kxeU7GD+0H6MH9406ikibVBREekDT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11144f278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(z, a)\n",
    "plt.xlabel(\"Z\")\n",
    "plt.ylabel(\"g(z)\")\n",
    "plt.title(\"Sigmoid\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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L3igWLZqRMnH1xeKKT7Li8rJIqg6IbDFU7g7zel5jTrFqVyMLJgzzLVn4KTMY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\nxpiY/H9u9VfX4F9mRgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113f2e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dz = a*(1-a)\n",
    "plt.plot(z, dz)\n",
    "plt.xlabel(\"Z\")\n",
    "plt.ylabel(\"g'(z)\")\n",
    "plt.title(\"Derivative of Sigmoid function\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tanh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tanh(z):\n",
    "    return (np.exp(z) - np.exp(-z)) / (np.exp(z) + np.exp(-z))\n",
    "\n",
    "z = np.linspace(-10, 10, 1000)\n",
    "a = tanh(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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42w/PpLJcf0YioIIikraT3T18/cm3mDmhmpt0qrDIO0I5y0ukmD3w4nZ2HT7O\no5+5nAptnYi8Q38NImnY3HKMexsa+aOLJnHlTN2VUSSRCopIik529/B3j61l1LBKvvqRuWHHESk4\n2uUlkgJ3559/tYEt+9t5+I73M656aNiRRAqOtlBEUnD/i9v52eo9/I8Pz2TB7AlhxxEpSCooIqfx\n8H/v4BtPb+aPLz6Lz15zXthxRAqWdnmJ9CMWc/7tN4185/mtXDe3hm9//GJ9I17kFFRQRPrQdqKb\nL/xsHc9u2s9HL53MN26+SF9gFDkNFRSRBO7Ok2/u46v/tYnDHV18+YY53PGBc7RlIpICFRQR4ru3\nfrO5le/+Zhvr97Rx4eRR/PDT7+fCyaPDjiZSNFRQZNBydza3tPP0hhZ+sWYPe46cYOrY4XzjY+/j\nY5dN0bfgRdIUSkExs48DdwMXAPPdfVU//RYB/wcoB37g7r13dhwL/AQ4B9gJfMLdj+Q8uBS1js4o\n2470sPO/d7B+Txu/bTzIgfZOzOADM8bxhetms/h9k3SsRCRDYW2hbAA+CjzQXwczKwfuJX4L4D3A\n62a2wt03AcuAF9z9HjNbFoz/Q+5jS5hiMaerJ0ZnNEZXNEZ3T/y5qydGR2eUthPdtJ3o5ljwfPR4\nN3vbTtB85ATNR09wMNIVLGkTZ1YN4YoZZ/KhWeO56rzxTBw9LNT3JlIKwroF8FvA6Q50zgca3X17\n0Hc5sATYFDwvCPo9AjSQw4Ly3Re2sfzl44xY8yLu/q4273fk3aOJ8yV1I3GRntT6rrbkGYGTJ08y\n7JXfZGf5p5gvsTU5R1/vs7u7m8qXnk1qe2+/Pl87afk97nRFY0RjfayAUxheWc6kMcOYPGY4c84a\nxZQzRtB9YCe3XPdBakYN1YF2kSwr5GMok4HdCeN7gMuD4Rp33xcMtwA1/S3EzJYCSwFqampoaGhI\nO8iRvd3UDI9RUXYivsxT9E1u6+8z6z2TLXHQ+mt6j+iQGJWV3afPdYpG62f4vblS79fd7VRWvrcA\nvGsZqWYyo7Ksgooy4g8zKsqgMhivLDOGlENVpVFVaYyojA9XlvUu5UTwOExkxEk2v/EKm/t/6VBE\nIpGMfjdzTbnSU6i5IE/Z3D0nD+B54ru2kh9LEvo0APP6mf9m4sdNesdvA74XDB9N6nsklUy1tbWe\nqfr6+oznzSXlSo9ypUe50lOoudwHlg1Y5Sl8xuZsC8XdFw5wEc3A1ITxKcE0gP1mNsnd95nZJKB1\ngK8lIiI1Iv1hAAAGlUlEQVQDVMins7wOzDKz6WY2BLgFWBG0rQBuD4ZvB34dQj4REUkQSkExs5vM\nbA/wB8CTZvZMMP0sM1sJ4O5R4C7gGeAt4KfuvjFYxD3ANWa2DVgYjIuISIjCOsvrceDxPqbvBRYn\njK8EVvbR7xBwdS4ziohIegp5l5eIiBQRFRQREckKFRQREckKFRQREckK876u51GizOwA8HaGs48D\nDmYxTrYoV3qUKz3KlZ5CzQUDyzbN3cefrtOgKigDYWar3H1e2DmSKVd6lCs9ypWeQs0F+cmmXV4i\nIpIVKigiIpIVKiipezDsAP1QrvQoV3qUKz2FmgvykE3HUEREJCu0hSIiIlmhgiIiIlmhgpLAzD5u\nZhvNLGZm85La/tHMGs1si5ld18/8Y83sOTPbFjyfkYOMPzGztcFjp5mt7affTjN7M+i3Kts5+ni9\nu82sOSHb4n76LQrWYaOZLctDrm+Z2WYzW29mj5vZmH765WV9ne79W9x3g/b1ZnZZrrIkvOZUM6s3\ns03B7//f9dFngZm1Jfx8v5zrXMHrnvLnEtL6mp2wHtaa2TEz+/ukPnlZX2b2kJm1mtmGhGkpfQ7l\n5G8xlbtwDZYHcAEwm6Q7SQJzgHXAUGA60ASU9zH/N4FlwfAy4Bs5zvtt4Mv9tO0ExuVx3d0NfP40\nfcqDdXcuMCRYp3NynOtaoCIY/kZ/P5N8rK9U3j/xq20/RfwuyFcAr+bhZzcJuCwYHgls7SPXAuCJ\nfP0+pfpzCWN99fEzbSH+xb+8ry/gKuAyYEPCtNN+DuXqb1FbKAnc/S1339JH0xJgubt3uvsOoBGY\n30+/R4LhR4Abc5M0/p8Z8AngsVy9Rg7MBxrdfbu7dwHLia+znHH3Zz1+bx2AV4jf+TMsqbz/JcCP\nPO4VYExwV9Kccfd97r4mGG4nfv+hybl8zSzK+/pKcjXQ5O6ZXoFjQNz9JeBw0uRUPody8reogpKa\nycDuhPE99P0HV+Pu+4LhFqAmh5n+ENjv7tv6aXfgeTNbbWZLc5gj0d8Gux0e6mczO9X1mCt/Tvy/\n2b7kY32l8v5DXUdmdg5wKfBqH81XBj/fp8xsbp4ine7nEvbv1C30/09dGOsLUvscysl6C+UGW2Ey\ns+eBiX00fcnds3YrYXd3M8vonOwUM97KqbdOPujuzWY2AXjOzDYH/81k7FS5gPuArxH/APga8d1x\nfz6Q18tGrt71ZWZfAqLAj/tZTNbXV7Exs2rgF8Dfu/uxpOY1wNnuHgmOj/0KmJWHWAX7c7H4rck/\nAvxjH81hra93GcjnUCYGXUFx94UZzNYMTE0YnxJMS7bfzCa5+75gs7s1FxnNrAL4KFB7imU0B8+t\nZvY48U3cAf0hprruzOz7wBN9NKW6HrOay8w+DdwAXO3BDuQ+lpH19dWHVN5/TtbR6ZhZJfFi8mN3\n/2Vye2KBcfeVZvbvZjbO3XN6IcQUfi6hrK/A9cAad9+f3BDW+gqk8jmUk/WmXV6pWQHcYmZDzWw6\n8f80Xuun3+3B8O1A1rZ4kiwENrv7nr4azazKzEb2DhM/ML2hr77ZkrTf+qZ+Xu91YJaZTQ/+u7uF\n+DrLZa5FwBeBj7j78X765Gt9pfL+VwB/Fpy9dAXQlrD7IieC43H/Abzl7v/aT5+JQT/MbD7xz45D\nOc6Vys8l7+srQb97CcJYXwlS+RzKzd9irs9CKKYH8Q/CPUAnsB94JqHtS8TPitgCXJ8w/QcEZ4QB\nZwIvANuA54GxOcr5MHBn0rSzgJXB8LnEz9pYB2wkvusn1+vuP4E3gfXBL+ak5FzB+GLiZxE15SlX\nI/F9xWuDx/1hrq++3j9wZ+/Pk/jZSvcG7W+ScLZhDjN9kPiuyvUJ62lxUq67gnWzjvjJDVfmIVef\nP5ew11fwulXEC8TohGl5X1/EC9o+oDv47PqL/j6H8vG3qEuviIhIVmiXl4iIZIUKioiIZIUKioiI\nZIUKioiIZIUKioiIZIUKikhIzOympKvWrrX4la6vDzubSCZ02rBIgQiuVfUpoM7dY2HnEUmXCopI\nATCz84DfEP8C3K6w84hkQru8REIWXEfrUeBzKiZSzLSFIhIyM7uH+KVqbj9tZ5ECNuiuNixSSMxs\nAfAx4nfdEylq2kIRCUlwE7I1wJ+4++/DziMyUNpCEQnPncAE4L7gSue9/sXdfxJOJJHMaQtFRESy\nQmd5iYhIVqigiIhIVqigiIhIVqigiIhIVqigiIhIVqigiIhIVqigiIhIVvw/LggwxbRnAMIAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11166a240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(z, a)\n",
    "plt.xlabel(\"Z\")\n",
    "plt.ylabel(\"g(z)\")\n",
    "plt.title(\"tanh\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Kykqn/u/SNFfNR5JsSgoik2idwoxrmZrqqjjZM0jf4HBBtidSaEoKIpM40tHPokIlhbCz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1116d0cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dz = 1 - (a ** 2)\n",
    "plt.plot(z, dz)\n",
    "plt.xlabel(\"Z\")\n",
    "plt.ylabel(\"g'(z)\")\n",
    "plt.title(\"Derivative of tanh\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Relu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def relu(z):\n",
    "    return np.maximum(0, z)\n",
    "\n",
    "z = np.linspace(-10, 10, 1000)\n",
    "a = relu(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EJK099O4CPlm8kd9dMpjDu+8XdBwhwp3FZlZtZr+2WvM3MyuOXywRSUfT11Xx+IdfcPnw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11189c828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(z, a)\n",
    "plt.xlabel(\"Z\")\n",
    "plt.ylabel(\"g(z)\")\n",
    "plt.title(\"relu\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JV+b33wNcJmlf4O4klZmZWce1FAoRca6kq4G/zBcti4hb8tsnJqnMrIt4otl6Ras9BfIQ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\nzAr/H5CJHFjstW2oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111b267b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dz = np.where(z <=0, 0, 1)\n",
    "plt.plot(z, dz)\n",
    "plt.xlabel(\"Z\")\n",
    "plt.ylabel(\"g'(z)\")\n",
    "plt.title(\"Derivative of relu\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Leaky Relu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def weak_relu(z):\n",
    "    return np.maximum(0.01 * z, z)\n",
    "\n",
    "z = np.linspace(-10, 10, 1000)\n",
    "a = weak_relu(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ws8XA/cDBoVUlIhUjExqbMv4wxgx4Ne5ypBP5bhH8R+aKuy8ifcL5K0KpSEQqRiY0dsJh\ne3PNqUfGXY50IWcjMLP3A7h7Y/b97t7s7v9jZu80s1FhFigi5SkTGttrj35MvXA0far1Qwalqrtd\nQxeY2feBPwCNwEbSgbLDgTpgOHBNqBWKSNnJDo3NuOx4hio0VtK6yxFcHXxL6ALg48C+pH9iYilw\nj7s/F36JIlJuftSwOzQ2RqGxktftwWJ332Rm7wQWAAszdwNHmVmLu88Ls0ARKS9PL9/Ifz+p0Fg5\nyXenXS0wGdiP9A/PXQacDvzEzL4SUm0iUmZWb97OlfVzFRorM/l+ffRAYIy7twCY2Y3A/wInkT52\n8P1wyhORcvHmmcbaXaGxMpPvFsEwYGfW7Vagxt13dLhfRBLq5t8tYcHqZm79xHsVGisz+W4RTAde\nMLNHgtsfAe43s4HAklAqE5Gy8avZTTzwt1VMGX8Yp71737jLkQLl1Qjc/RYz+z3pk9MATHb32cH1\ni0OpTETKwuK1zVyv0FhZy/vk9cGKf3a3I4pIYjRvb2XyNIXGyl3ejUBEJFsq5Vz94DyFxiqA2reI\nFOWOhpU89dIGvnH2SIXGypwagYgU7OnlG/nBk8s575j9uUShsbIXWyMws2ozm2tmj8VVg4gULhMa\nO3LYYL59vkJjlSDOLYIrSf9mkYiUiezQ2N2X1LJHPx1mrASxNAIzOxA4i/QZz0SkTGRCY/+l0FhF\nMffozzhpZg8B3wEGA19y97M7GWcSMAmgpqamtr6+vqh5tbS0MGjQoB5UGw7VVRjVVZgw6np2dSv3\nLtrFmYf05RNH9SuZunpDqdYFPautrq6u0d3Hdjuiu0d6Ac4G7gyujwce6+4xtbW1XqyGhoaiHxsm\n1VUY1VWY3q5r0ZotfuR1j/uEe/7qrW3tRU8nKcurN/WkNmC257FejmPX0InAOWb2ClAPfMjMpsVQ\nh4jkITs0dvtFCo1VoshfUXf/mrsf6O4jgAnAU+4+Meo6RKR72aGxOy4eo9BYhVJrF5EuZYfGaocr\nNFapYv3ul7vPAmbFWYOIdO4ZhcYSQ1sEIvI2Co0lixqBiLzFzrZ2Pjd9Dm0KjSWGXmEReYubf7eE\n+aubueeSWoXGEkJbBCLypocaV3P/C6uY/MHD+LDONJYYagQiAqTPNHbdbxZy/KF786XTdKaxJFEj\nEBGat7cyZdochcYSSscIRBIulXK++OA81jXvoH6SzjSWRGr7Igl356yVzHxpA9efpdBYUqkRiCTY\nM8s3cusTyzn3mP355PEKjSWVGoFIQmWHxr6j0FiiqRGIJFB2aOyuiWMUGks4vfoiCZQJjd09sZZD\n9ynNE7JIdLRFIJIwmdDYZR88lNNHKTQmagQiiZIdGvvyaUfFXY6UCDUCkYRQaEy6omMEIgmg0Jjk\noo8EIgmg0JjkokYgUuGeXaHQmOSmRiBSwdZs2cEVDyg0JrmpEYhUqJ1t7Vw+rVGhMemW3hkiFeo/\nFRqTPKkRiFSgP69pZfpChcYkP9o1JFJhlqzdys8X71JoTPKmRiBSQZp3tDJleiMD+xpTL1RoTPKj\nd4lIhUilnGsenMeazTv43DH92WewQmOSHzUCkQpx19Mv8+TSDVx/1tEcsVd13OVIGVEjEKkAz67Y\nyK1/WsY5792fS08YEXc5UmbUCETKXCY0dviwQXz3AoXGpHBqBCJlLBMaa2137p5Yq9CYFEXvGpEy\nptCY9IbItwjM7CAzazCzJWa22MyujLoGkUrwcONqputMY9IL4tgiaAOucfc5ZjYYaDSzJ9x9SQy1\niJSlJWu38nWdaUx6SeRbBO6+zt3nBNdfB5YCB0Rdh0i5yoTG9tyjr0Jj0ivM3eObudkI4BlglLtv\n7TBsEjAJoKampra+vr6oebS0tDBoUOntO1VdhVFdaSl3ps7ZycLX2rl23IAu8wJaXoUp1bqgZ7XV\n1dU1uvvYbkd091guwCCgETi/u3Fra2u9WA0NDUU/NkyqqzCqK+1HT63w4V99zH/23N9zjqflVZhS\nrcu9Z7UBsz2P9XEs25Rm1hd4GJju7r+OowaRcvPcitcUGpNQxPGtIQPuBZa6+w+inr9IOVq7ZQdX\n1Cs0JuGIY4vgROAS4ENmNi+4nBlDHSJlYWdbO1Omz2FXW0qhMQlF5O8od38O0McZkTzd8tgS5jdt\n4e6JYxQak1Doe2ciJezXc1Yz7flVXHbSoZw+ar+4y5EKpUYgUqKWrkuHxo47dAhf/rBCYxIeNQKR\nEtS8o5XJ0xp51zv6cvuFYxQak1DpqJNIiUmfaWw+azbvYMZlx+lMYxI6fcwQKTHpM42t57qzjqZ2\n+JC4y5EEUCMQKSF/Xrk7NPYphcYkImoEIiVi7ZYdfCE409h3zldoTKKjRiBSAjqGxgb21+E7iY7e\nbSIlQKExiZO2CERiptCYxE2NQCRGCo1JKVAjEImJQmNSKnSMQCQGCo1JKdFHEJEYKDQmpUSNQCRi\nCo1JqVEjEIlQJjR22D4KjUnpUCMQicjOtnYuz4TGLlFoTEqH3okiEfnmY0uZ17SFuy4ew2EKjUkJ\n0RaBSAR+M3c1v3z+/5h00qGc8R6FxqS0qBGIhGzpuq187dcLOfaQIXxFoTEpQWoEIiFq3tHKlGmN\nvHNAX26/aLRCY1KSdIxAJCSplPOlX81n9eYd1E86jmGDB8Rdkkin9PFEJCR3P/MyTyxJh8bGjlBo\nTEqXGoFICP688jX+648KjUl5UCMQ6WXrmndwhUJjUkbUCER60c62dqZMm8NOhcakjOhdKtKLFBqT\ncqQtApFeotCYlCs1ApFeoNCYlDM1ApEeUmhMyl0s71gzO93MlpnZSjO7No4aRHpDyneHxu68eIxC\nY1KWIm8EZlYN3AGcAYwELjSzkVHXIdIbHv9HK08sWc/Xz1RoTMpXHN8aGgesdPe/A5hZPXAusCSG\nWqSXuDsph/aUpy/uu6+nnFSH250Nb0s5qU7GSbkzb30bbyxaR3sK2lKpYHrQnkql/3r6sW9Oo5vp\nt2XVlHKnrd3fOo231UswLEUqmF9re4oFq1s5+1/349Mnjoj7JRApmrl7tDM0+xhwurv/R3D7EuBY\nd/98h/EmAZMAampqauvr64uaX0tLC4MGFfY1vlSwUuv8EqwUHJz03/asYd09LvOYbTveoF//Aenp\nZE3zbRecVApSWfNyz1zfPT9/Sx1ZtdB5Ldm335wm0NrWDlVVXT6HzmtM/y1lBlRZ+lJtYJZ926iy\n9DjVVenN5Ko3h1vW9Y7TMPbs08bEUQMZ0Ke0QmPFvO+joLoK15Pa6urqGt19bHfjlWyOwN1/DPwY\nYOzYsT5+/PiCpzF15goemLuC/gMyn/bSnybbU+T8hBoNA3YW/qjMiqvK6FNlb7leFdyurtp9qTLo\nU1VFVbVRXQXVVVX0NYJhRp/q9N/qYBqb/vlPaobtU8D03zps9/R4c1h1VdY0Ojy+s+m/eT1r+nPn\nNDLufe97S73VZlRXZ6aRfp7Z16uqeLPesNK9s2bNopj3ZthUV2FKtS6IprY4GsEa4KCs2wcG9/W6\nYYP7c9DgKvat2fNtK57qzMrCdq8gq6vodsX3lml0WJFWZ42fe8UHcxsbOe7Y9wUrumCl1d00gvmG\nKf2mqw11HsXY/HI1I/d/Z9xliFSkOBrBi8ARZnYI6QYwAbgojBlNGHcw+27/O+PHjw5j8j2ycXkV\nhw8bHHcZIiLRNwJ3bzOzzwN/BKqB+9x9cdR1iIhIWizHCNz9ceDxOOYtIiJvpQikiEjCqRGIiCSc\nGoGISMKpEYiIJJwagYhIwqkRiIgkXOS/NVQMM9sI/F+RDx8KvNaL5fQW1VUY1VUY1VWYUq0Lelbb\ncHffp7uRyqIR9ISZzc7nR5eiproKo7oKo7oKU6p1QTS1adeQiEjCqRGIiCRcEhrBj+MuoAuqqzCq\nqzCqqzClWhdEUFvFHyMQEZHckrBFICIiOagRiIgkXEU0AjP7uJktNrOUmY3tMOxrZrbSzJaZ2Ye7\nePwQM3vCzFYEf/cKocYZZjYvuLxiZvO6GO8VM1sYjDe7t+voZH43mdmarNrO7GK804NluNLMro2g\nrv9nZi+Z2QIz+42Z7dnFeJEsr+6ev6VNDYYvMLMxYdWSNc+DzKzBzJYE7/8rOxlnvJk1Z72+N4Rd\nVzDfnK9LTMvrqKzlMM/MtprZVR3GiWR5mdl9ZrbBzBZl3ZfXeiiU/0V3L/sLcDRwFDALGJt1/0hg\nPtAfOAR4Gaju5PHfB64Nrl8LfC/kem8Fbuhi2CvA0AiX3U3Al7oZpzpYdocC/YJlOjLkuk4D+gTX\nv9fVaxLF8srn+QNnAr8nfTLq44AXInjt9gPGBNcHA8s7qWs88FhU76d8X5c4llcnr+mrpANXkS8v\n4CRgDLAo675u10Nh/S9WxBaBuy9192WdDDoXqHf3ne7+D2AlMK6L8X4RXP8FcF44laY/CQGfAB4I\nax4hGAesdPe/u/suoJ70MguNu//J3duCm8+TPrd1XPJ5/ucC/+NpzwN7mtl+YRbl7uvcfU5w/XVg\nKXBAmPPsRZEvrw5OBl5292J/saBH3P0ZYFOHu/NZD4Xyv1gRjSCHA4CmrNur6fwfpcbd1wXXXwVq\nQqzpA8B6d1/RxXAHnjSzRjObFGId2b4QbJ7f18XmaL7LMSz/TvrTY2eiWF75PP9Yl5GZjQBGAy90\nMviE4PX9vZm9O6KSuntd4n5PTaDrD2NxLC/Ibz0UynKL5VSVxTCzJ4F9Oxl0nbs/0lvzcXc3s6K+\nU5tnjReSe2vg/e6+xsyGAU+Y2UvBp4ei5aoLuAu4hfQ/7i2kd1v9e0/m1xt1ZZaXmV0HtAHTu5hM\nry+vcmNmg4CHgavcfWuHwXOAg929JTj+81vgiAjKKtnXxcz6AecAX+tkcFzL6y16sh4qRtk0Anc/\npYiHrQEOyrp9YHBfR+vNbD93Xxdsnm4Io0Yz6wOcD9TmmMaa4O8GM/sN6U3BHv0D5bvszOwnwGOd\nDMp3OfZqXWb2KeBs4GQPdpB2Mo1eX16dyOf5h7KMumNmfUk3genu/uuOw7Mbg7s/bmZ3mtlQdw/1\nB9byeF1iWV6BM4A57r6+44C4llcgn/VQKMut0ncNPQpMMLP+ZnYI6c7+ty7GuzS4finQa1sYHZwC\nvOTuqzsbaGYDzWxw5jrpA6aLOhu3t3TYL/vRLub3InCEmR0SfJqaQHqZhVnX6cBXgHPcfXsX40S1\nvPJ5/o8Cnwy+DXMc0Jy1mR+K4HjTvcBSd/9BF+PsG4yHmY0j/T//z5Dryud1iXx5ZelyqzyO5ZUl\nn/VQOP+LYR8dj+JCegW2GtgJrAf+mDXsOtJH2ZcBZ2Td/1OCbxgBewMzgRXAk8CQkOr8OTC5w337\nA48H1w8l/S2A+cBi0rtIwl52vwQWAguCN9R+HesKbp9J+lspL0dU10rS+0LnBZe741xenT1/YHLm\n9ST97Zc7guELyfr2Wog1vZ/0Lr0FWcvpzA51fT5YNvNJH3Q/IYK6On1d4l5ewXwHkl6xvyvrvsiX\nF+lGtA5oDdZdn+lqPRTF/6J+YkJEJOEqfdeQiIh0Q41ARCTh1AhERBJOjUBEJOHUCEREEk6NQKRA\nZvbRDr9iOc/Sv3x7Rty1iRRDXx8V6aHgt3QuBurcPRV3PSKFUiMQ6QEzOxJ4inTwaFXc9YgUQ7uG\nRIoU/M7P/cA1agJSzrRFIFIkM/su6Z/kuLTbkUVKWNn8+qhIKTGz8cAFpM8yJVLWtEUgUqDg5D1z\ngIvc/a9x1yPSU9oiECncZGAYcFfwi8UZ33H3GfGUJFI8bRGIiCScvjUkIpJwagQiIgmnRiAiknBq\nBCIiCadGICKScGoEIiIJp0YgIpJw/x+UzKf3tA6xeQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111ac3550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(z, a)\n",
    "plt.xlabel(\"Z\")\n",
    "plt.ylabel(\"g(z)\")\n",
    "plt.title(\"Weak relu\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
